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Math 1314
Review for Final Exam
I.
Limits
1.
Evaluate:
2
3
lim 2
3
9
x
x
x
→

+
2.
Evaluate:
2
2
4
2
8
lim
16
x
x
x
x
→



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View Full Document 3.
Find
1
1
lim
( ), lim
x
x
f x

+
→
→
and
1
lim
( )
x
f x
→
given the graph
below:
4
3
2
1
1
2
3
4
5
4
3
2
1
1
2
3
4
x
y
4.
Suppose
2
2
3,
2
( )
5,
2
1
3,
1
x
x
f x
x
x
x
+
< 
=

 ≤
≤
Find
2
2
2
1
lim
( ), lim
( ), lim
( ), lim
( )
x
x
x
x
f x
f x
f x
f x
+

+
→
→
→
→
1
1
lim
( ), lim ( )
x
x
f x
f x

→
→
5.
Evaluate:
2
2
3
6
3
lim
4
x
x
x
x
→∞

+
+
.
6.
Evaluate:
2
3
lim
5
2
4
x
x
x
x
→∞

+

.
Find Derivatives
7.
Find the derivative:
4
3
2
( )
5
3
8
7
1
f x
x
x
x
x
=

+

+
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View Full Document 8.
Find the derivative:
4
( )
7
x
f x
x
e
x
=
+
+
9.
Find the derivative:
2
( )
ln
f x
x
x
=
10.
Find the derivative:
( 29
2
( )
ln 4
3
f x
x
=
+
11.
Find the derivative:
2
3
( )
2
5
x
f x
x
+
=

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View Full Document 12.
Find the derivative:
4
( )
3
x
f x
e

=
14.
Find the second derivative:
3
2
( )
3
8
5
3
f x
x
x
x
=

+
+
15.
Find the second derivative:
( 29
4
5
( )
3
f x
x
=

16.
Find the equation of the line tangent to
3
( )
4 5
3
f x
x
x
= 

at the point (1, 12).
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View Full Document 17.
Population is growing according to the model
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This note was uploaded on 02/21/2012 for the course MATH 1314 taught by Professor Marks during the Fall '08 term at University of Houston.
 Fall '08
 MARKS

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